Problem
COM-B1-M08-P011 Rooks on \(7\times7\)
#11
★★☆☆☆ Level 2 of 5
Players alternately place rooks on a \(7\times7\) board so that no two rooks share a row or column. A player who cannot move loses. Who wins?
How many moves does the game last regardless of choices?
After \(k\) moves, exactly \(k\) rows and \(k\) columns are occupied. If \(k<7\), a free row and a free column remain, and a rook can be placed at their intersection. Thus the game always lasts exactly \(7\) moves. The seventh move is made by the first player, so the first player wins.
No specific first square is needed.